68 ON MAGNETISM. 



Let the probable error of D x be e v and the probable error 

 of Z> 2 be e z (see the Author's Treatise on 'Errors of 

 Observations/ Article 28) : then the square of the pro- 

 bable error of the expression for # will be (see Articles 

 44 and 50 of the same treatise) 



(c;*v-v.o^x C 2 " 10 x e>(cf X~ 5 -^~WTX~ 10 >< & 



and if e l = e 2 = e, the square of the probable error of x 



= (of 3 - <** - or*- <vT x (cf 10 + o x e. 



A value of c 2 is to be found which will make this 

 minimum. Differentiating with respect to c 2 and making 



s\ 



the differential coefficient = 0, and putting z for -, this 



c i 

 equation is obtained, 



53 10 -3-2 12 + 23 2 = 0; 

 of which the solution is 



st 



z or = 1*32 very nearly. 

 c i 



It is usual in the best modern instruments to make 

 C 2 = Cj x 1-3. 



31. Incidental inference as to the effect of tempera- 

 ture upon the magnet-power of the disturbing magnet, 

 and necessity for correction for temperature in various 

 experiments. 



In considering the deflexion-experiments made 

 under different atmospheric temperatures, it is found 

 that the proportion of magnet-power of the disturbing 

 magnet to that of the earth is smallest at the highest 

 temperatures. To measure the amount of change for 



